What is the reason these two UV maps interfere with each other?
The problem is that your UVMap Face 1 is actually mapping the Face 1.png


In your list of UV Maps, select the UVMap Face 1.
In the 3D view, select all the faces except the dice face 1.
In the UV/Image editor, press W twice (Weld) and move the dot to some where safe(transparent)


That'll resolve your problem.